The Only One (Unique)
Modern Greek lexicons has μονογενής (monogenēs) having two primary definitions:
(i) pertaining to being the only one of its kind within a specific relationship and.
(ii) pertaining to being the only one of its kind or class, unique in kind"
(Source: Greek-English Lexicon of the New Testament and Other Early Christian Literature (BAGD, 3rd Edition)).
According to scholars, μονογενής is merely a fuller form of monos:
(God's Only Son: The Translation of John 3:16 in the Revised Standard Version, Dale Moody, 1953).
Only Begotten
It is commonly said that the rendering of μονογενης as unigenitus only started in the fourth century. However, we have evidence that μονογενης was understood as ''only begotten/uniquely begotten'' in the second century in Greek and in Latin.
Native Greek speaking Christians in the 2nd century C.E. understood γενής in μονογενής as "begotten''. Tertullian spoke of Christ as "unigenitus because alone genitus of God [Against Praxeas VII]. The Greek fathers like Justin Martyr used μονογενες in the context of the begetting of the Son before all creatures (Dialogue to Trypho, 105).
In the 2nd century A.D., the church fathers spoke of Jesus as ''only begotten'' before all creatures/ before the ages. In this case, μονογενες is understood as ''only begotten'' because no other son is begotten of God from eternity. However, in the Gospel of John, μονογενες (1:14, 1:18) occurred in close proximity with other sons who were also described as ''begotten'' (ἐγεννήθησαν) of God (John 1:12-13). In this case, μόνος in μονογενες should be seen as ''unique'' (i.e. alone of its kind, single in category): ''uniquely begotten.''
